REEBY SPORTS
Minicase solution, Chapter 4
Principles of Corporate Finance, 12th Edition
R. A. Brealey, S. C. Myers and F. Allen
What is Reeby Sports worth per share? We will value the company using George
Reeby's forecasts.
The spreadsheet accompanying this solution sets out a forecast in the same
general format as Table 4.5. Historical results from 2011 to 2016 are also shown.
Earnings per share (EPS) equals return on equity (ROE) times starting book value per
share (BVPS). EPS is divided between dividends and retained earnings, depending on
the dividend payout ratio. BVPS grows as retained earnings are reinvested.
The keys to Reeby Sports’ future value and growth are profitability (ROE) and
the reinvestment of retained earnings. Retained earnings are determined by dividend
payout. The spreadsheet sets ROE at 15% for the six years from 2018 to 2022. If Reeby
Sports will lose its competitive edge by 2022, then it cannot continue earning more than
its 10% cost of capital. Therefore ROE is reduced to 10% starting in 2023.1
The payout ratio is set at .30 from 2018 onwards. Notice that the long-term
growth rate, which settles in after 2023, is ROE × ( 1 – dividend payout ratio) = .10 × (1 -
.30) = .07.
The spreadsheet allows you to vary ROE and the dividend payout ratio separately
for 2018-2022 and for 2023-2024.2 But let’s start with the initial input values. To
calculate share value, we have to estimate a horizon value at H = 2022 and add its PV to
the PV of dividends from 2017 to 2022. Using the constant-growth DCF formula,
0.71
PVH = = 23.72
.10 - .07
The PV of dividends from 2017 to 2022 is $3.43 at the start of 2017, so share value is:3
1
A more sophisticated spreadsheet could distinguish ROE on existing assets from ROE on new capital
investment. For example, ROE on new investment could drop all the way to 10% in 2020, but ROE for
existing assets could decline gradually.
2
You can vary these inputs, but be careful not to enter ROEs and dividend payout ratios that generate long-
term growth rates close to or above the cost of capital. As the growth rate approaches the cost of capital,
the DCF formula explodes. If the growth rate exceeds the cost of capital, the DCF formula says stock price
is negative, which is impossible. The spreadsheet reports “Formula not applicable” in this case.
3
This DCF calculation assumes that the first dividend will be received after one year, at the end of 2017.
Normally dividends are paid quarterly, so it would be more realistic to assume receipt at the middle of the
year. This “mid-year convention” would move all cash flows 6 months closer and therefore increase PV by
1.1.5. (In finance, “mid-year convention” does not mean June in Las Vegas.)
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, 23.72
PV = 3.43 + = $16.82
(1.1)6
The spreadsheet also calculates the PV of dividends through 2024 and the horizon
value at 2024. Notice that the PV at the start of 2017 remains at $16.82. This makes
sense, since the value of a firm should not depend on the investment horizon chosen to
calculate PV. (If you calculate a value that does depend on the horizon, you have made a
mistake.)
We have reduced ROE to the 10% cost of capital after 2022, assuming that Reeby
Sports will have exhausted valuable growth opportunities by that date. With PVGO = 0,
PV = EPS/r. 4 So we could discard the constant-growth DCF formula and just divide
EPS in 2023 by the cost of capital:
2.37
PVH = = $23.72
.10
This PV is identical to the PV from the constant-growth DCF formula. It doesn’t matter
how fast a company grows after the horizon date H if it only earns its cost of capital.
How much of Reeby Sports’ value is due to PVGO? You can check by setting
ROE = .10 for 2018 and all later years. You should get PV = $13.82. Thus PVGO =
16.82 – 13.82 = $3.00 per share for investments made in 2017 onward.
George Reeby has also identified a "comparable," Molly Sports. We could use its
P/E ratio of 13.1 to calculate horizon value in 2022 and PV at the start of 2017. Using
the original inputs for ROE, EPS in 2023 is 2.37.5
PVH = 13.1 × 2.37 = $31.05
31.05
PV = 3.43 + = $20.96
(1.10)6
We could also use Molly’s P/E ratio to calculate Reeby Sports’ PV at the start of 2017
directly from 2017 EPS:
PV = 13.1 × 2.03 = $26.59
4
See Section 4.5.
5
Notice that the P/E ratio applies to the next year’s forecasted earnings. Sometimes “trailing P/Es” are
used instead. Trailing P/Es are based on earnings over the previous year.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, Both values based on Molly’s P/E are higher than our DCF calculations. Is Molly
significantly more profitable than Reeby Sports, or does our spreadsheet understate
Reeby Sports’ prospects?
What if Reeby Sports could continue to earn ROE = .15 for two extra years, until
2024? You can check by changing ROE for 2023-2024 from .10 to .15. (The ROE for
2025 and 2026 is hard-wired at .10.) You should get NPV of $18.04, somewhat higher
than our original DCF calculations, but not enough for Reeby Sports to match Molly’s
P/E. You may wish to experiment to find inputs that generate P/E = 13 for Reeby Sports
at the start of 2017. Do you think these inputs are reasonable?
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, VEGETRON’S CFO CALLS AGAIN
Minicase solution, Chapter 5
Principles of Corporate Finance, 12th Ed.
R. A. Brealey, S. C. Myers and F. Allen
The high-temperature process produces $110,000 per year for 5 years. The low-
temperature process produces $85,000 per year for 7 years. Each costs $400,000. The
NPVs (at 9%) and IRRs are:
NPV IRR
High-temperature +$28,000 11.7%
Low-temperature +$28,000 11%
The NPVs are identical. The high-temperature process has a slightly higher IRR because
of its quicker payback.
The CFO returns 30 minutes later:
CFO: What did you find out?
You: It’s a dead heat. The two projects are equally valuable. NPV is +$28,000 for each.
The high-temperature process has a slightly higher DCF rate of return, but that’s typical
of quick-payback projects. It doesn’t mean that the high-temperature process generates
more value for the firm and its stockholders.
CFO: And the book rates of returns are irrelevant?
You: Yes. There’s not a single year when the book rate of return matches the true, DCF
rate of return. Average book returns – for example the ratio of average income to average
book investment – don’t measure the true rate of return. Book rates of return don’t help at
all in making good capital investment decisions.
CFO: Let’s stick with the low-temperature process. I’m not 100% confident that the
high-temperature process will work.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
Minicase solution, Chapter 4
Principles of Corporate Finance, 12th Edition
R. A. Brealey, S. C. Myers and F. Allen
What is Reeby Sports worth per share? We will value the company using George
Reeby's forecasts.
The spreadsheet accompanying this solution sets out a forecast in the same
general format as Table 4.5. Historical results from 2011 to 2016 are also shown.
Earnings per share (EPS) equals return on equity (ROE) times starting book value per
share (BVPS). EPS is divided between dividends and retained earnings, depending on
the dividend payout ratio. BVPS grows as retained earnings are reinvested.
The keys to Reeby Sports’ future value and growth are profitability (ROE) and
the reinvestment of retained earnings. Retained earnings are determined by dividend
payout. The spreadsheet sets ROE at 15% for the six years from 2018 to 2022. If Reeby
Sports will lose its competitive edge by 2022, then it cannot continue earning more than
its 10% cost of capital. Therefore ROE is reduced to 10% starting in 2023.1
The payout ratio is set at .30 from 2018 onwards. Notice that the long-term
growth rate, which settles in after 2023, is ROE × ( 1 – dividend payout ratio) = .10 × (1 -
.30) = .07.
The spreadsheet allows you to vary ROE and the dividend payout ratio separately
for 2018-2022 and for 2023-2024.2 But let’s start with the initial input values. To
calculate share value, we have to estimate a horizon value at H = 2022 and add its PV to
the PV of dividends from 2017 to 2022. Using the constant-growth DCF formula,
0.71
PVH = = 23.72
.10 - .07
The PV of dividends from 2017 to 2022 is $3.43 at the start of 2017, so share value is:3
1
A more sophisticated spreadsheet could distinguish ROE on existing assets from ROE on new capital
investment. For example, ROE on new investment could drop all the way to 10% in 2020, but ROE for
existing assets could decline gradually.
2
You can vary these inputs, but be careful not to enter ROEs and dividend payout ratios that generate long-
term growth rates close to or above the cost of capital. As the growth rate approaches the cost of capital,
the DCF formula explodes. If the growth rate exceeds the cost of capital, the DCF formula says stock price
is negative, which is impossible. The spreadsheet reports “Formula not applicable” in this case.
3
This DCF calculation assumes that the first dividend will be received after one year, at the end of 2017.
Normally dividends are paid quarterly, so it would be more realistic to assume receipt at the middle of the
year. This “mid-year convention” would move all cash flows 6 months closer and therefore increase PV by
1.1.5. (In finance, “mid-year convention” does not mean June in Las Vegas.)
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, 23.72
PV = 3.43 + = $16.82
(1.1)6
The spreadsheet also calculates the PV of dividends through 2024 and the horizon
value at 2024. Notice that the PV at the start of 2017 remains at $16.82. This makes
sense, since the value of a firm should not depend on the investment horizon chosen to
calculate PV. (If you calculate a value that does depend on the horizon, you have made a
mistake.)
We have reduced ROE to the 10% cost of capital after 2022, assuming that Reeby
Sports will have exhausted valuable growth opportunities by that date. With PVGO = 0,
PV = EPS/r. 4 So we could discard the constant-growth DCF formula and just divide
EPS in 2023 by the cost of capital:
2.37
PVH = = $23.72
.10
This PV is identical to the PV from the constant-growth DCF formula. It doesn’t matter
how fast a company grows after the horizon date H if it only earns its cost of capital.
How much of Reeby Sports’ value is due to PVGO? You can check by setting
ROE = .10 for 2018 and all later years. You should get PV = $13.82. Thus PVGO =
16.82 – 13.82 = $3.00 per share for investments made in 2017 onward.
George Reeby has also identified a "comparable," Molly Sports. We could use its
P/E ratio of 13.1 to calculate horizon value in 2022 and PV at the start of 2017. Using
the original inputs for ROE, EPS in 2023 is 2.37.5
PVH = 13.1 × 2.37 = $31.05
31.05
PV = 3.43 + = $20.96
(1.10)6
We could also use Molly’s P/E ratio to calculate Reeby Sports’ PV at the start of 2017
directly from 2017 EPS:
PV = 13.1 × 2.03 = $26.59
4
See Section 4.5.
5
Notice that the P/E ratio applies to the next year’s forecasted earnings. Sometimes “trailing P/Es” are
used instead. Trailing P/Es are based on earnings over the previous year.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, Both values based on Molly’s P/E are higher than our DCF calculations. Is Molly
significantly more profitable than Reeby Sports, or does our spreadsheet understate
Reeby Sports’ prospects?
What if Reeby Sports could continue to earn ROE = .15 for two extra years, until
2024? You can check by changing ROE for 2023-2024 from .10 to .15. (The ROE for
2025 and 2026 is hard-wired at .10.) You should get NPV of $18.04, somewhat higher
than our original DCF calculations, but not enough for Reeby Sports to match Molly’s
P/E. You may wish to experiment to find inputs that generate P/E = 13 for Reeby Sports
at the start of 2017. Do you think these inputs are reasonable?
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
, VEGETRON’S CFO CALLS AGAIN
Minicase solution, Chapter 5
Principles of Corporate Finance, 12th Ed.
R. A. Brealey, S. C. Myers and F. Allen
The high-temperature process produces $110,000 per year for 5 years. The low-
temperature process produces $85,000 per year for 7 years. Each costs $400,000. The
NPVs (at 9%) and IRRs are:
NPV IRR
High-temperature +$28,000 11.7%
Low-temperature +$28,000 11%
The NPVs are identical. The high-temperature process has a slightly higher IRR because
of its quicker payback.
The CFO returns 30 minutes later:
CFO: What did you find out?
You: It’s a dead heat. The two projects are equally valuable. NPV is +$28,000 for each.
The high-temperature process has a slightly higher DCF rate of return, but that’s typical
of quick-payback projects. It doesn’t mean that the high-temperature process generates
more value for the firm and its stockholders.
CFO: And the book rates of returns are irrelevant?
You: Yes. There’s not a single year when the book rate of return matches the true, DCF
rate of return. Average book returns – for example the ratio of average income to average
book investment – don’t measure the true rate of return. Book rates of return don’t help at
all in making good capital investment decisions.
CFO: Let’s stick with the low-temperature process. I’m not 100% confident that the
high-temperature process will work.
Copyright © 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
